MAT6017 Differential Equations IIBahçeşehir UniversityDegree Programs MATHEMATICS (TURKISH, PHD)General Information For StudentsDiploma SupplementErasmus Policy StatementNational Qualifications
PhD TR-NQF-HE: Level 8 QF-EHEA: Third Cycle EQF-LLL: Level 8

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT6017 Differential Equations II Fall 3 0 3 8
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Prof. Dr. CANAN ÇELİK KARAASLANLI
Recommended Optional Program Components: None
Course Objectives: Bu ders doğrusal olmayan sistemleri veya adi diferansiyel denklemlerin çalışmasına ayrılmıştır.Birincil amaç, değişmez setler dahil olmak üzere ve diferansiyel denklemler sistemi tarafından tanımlanan dinamik sistem veya akış davranışını sınırlayan diferansiyel denklemlerin bir sistemin niteliksel davranışını tanımlamaktır.

Learning Outcomes

The students who have succeeded in this course;
1. To learn and solve the nonlinear systems
2. To learn the fundamental Existence and Uniqueness theorem
3. To learn the local theory of dynamical systems

Course Content

Nonlinear Systems: Lokal Theory, Fundamental existence theorem, dependence on initial conditions and parameters, the maximal interval of existence, Flow defined by a differential equation. Linearization, stable manifold theorem, Hartman-Grobman theorem, Stability and Liapunov functions, Saddles, Nodes, Foci and centers, Nonhyperbolic critical points in R^2, Center Manifold and Normal form Theory, Gradient and Hamiltonian system.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Nonlinear systems: Basic definiitons and concepts.
2) The Fundamental Existence-Uniqueness Theorem
3) Dependence on Initial Conditions and Parameters
4) The Maximal Interval of Existence
5) The Flow Defined by a Differential Equation
6) Linearization
7) The Stable Manifold Theorem
8) The Hartman-Grobman Theorem
10) Stability and Liapunov Functions
11) Saddles, Nodes, Foci and Centers
12) Nonhyperbolic Critical Points
13) Center Manifold and Normal form Theory
14) Gradient and Hamiltonian Systems.


Course Notes / Textbooks: Differential Equations and Dynamical Systems, Lawrence Perko
References: Ordinary Differential Equations,Jack K. Hale

Hirsch and Smale – Differential Equations, Dynamical Systems,
and Liner Algebra - Academic Press, New York, (1974)

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Homework Assignments 3 % 10
Midterms 1 % 40
Final 1 % 50
Total % 100
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Study Hours Out of Class 3 20 60
Homework Assignments 3 15 45
Midterms 1 23 23
Final 1 30 30
Total Workload 200

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
Program Outcomes Level of Contribution